Shares in Aflac (AFL), the life and health insurer that does three-quarters of its business in Japan, tumbled 7% Tuesday. The Columbus, Ga., company has lost more than $3 billion of market value since Japan was hit Friday by a 9.0-magnitude earthquake and tsunami.

The latest slide in Aflac shares comes amid fears that nuclear reactors hit by the tsunami will melt down, sickening thousands and saddling Aflac with massive claims.

That sounds plausible, but executives say it doesn’t jibe with the company’s catastrophe experience — or with the health impacts of the worst-ever nuclear accident two decades ago.

“I’m not surprised our stock has gotten hit,” said CEO Dan Amos. “Uncertainty creates panic, and that’s what we’re seeing today. But the numbers are not what people think.”

Executives say Aflac is unlikely to face costly claims exposures, due to limited exposure to the quake area and its habit of writing policies with low face values.

Amos notes that Aflac derives just 5% of its revenue from the regions hit by the quake and tsunami. That number drops to 1.5% or so if you focus on the harder-hit coastline.

Chief actuary Sue Blanck notes that Aflac covered claims in two recent megadisasters – the Sept. 11, 2001, terrorist attacks and Hurricane Katrina four years later – by setting aside just $3 million or so in total.

She says Aflac will continue to assess its exposure to health and life insurance claims in Japan over the next month or so, before it closes out its first-quarter books. But she says so far that “there is nothing to indicate a lot of long-term impacts” – which explains why Aflac said Monday that it expects to hit sales and earnings targets it set last year.

That’s not to say the company is taking the disaster lightly. “We are going to watch it day by day,” Amos said.

But there are signs that the investors fleeing Aflac may misunderstand the claims implications should a large radiation leak occur.

“We don’t believe Japan will be a Chernobyl,” Amos said. But he adds that as horrific as Chernobyl was, a 2005 United Nations study showed that fewer than 50 deaths could be attributed to the 1986 disaster – almost all of them among rescue workers.

The study estimated that 4,000 people will eventually die of radiation-related illnesses. But the fact that few of those deaths have occurred more than two decades after the event suggests claims will be limited.

Sterne Agee analyst John Nadel, who rates the stock buy, says that timing is likely to work out in Aflac’s favor.

While death claims would be an immediate impact, we note that any impact from supplemental medical and/or cancer (should radiation become a health risk) would take years to develop. Importantly, all of AFL’s supplemental medical and cancer insurance policies provide fixed-benefits. In other words, frequency of claim, rather than severity, would be the driver of any negative impact on profitability. And even in the event that frequency spiked 10% or 20%, the present value of such an impact would be modest.

Amos, for his part, is crossing his fingers that we won’t end up finding out what the worst case looks like.

“Our thoughts and prayers are with the Japanese people,” he said. “Our job is to be there to pay claims, and that’s what we’re going to do.”

Also on Fortune.com:

• Sagging stocks put Bernanke on the spot
• In Japan, fending off the unthinkable
• Avoid knee-jerk, anti-nuke moves

Follow me on Twitter at @ColinCBarr.